Blender non square unwrap
The diagonal line comes from the way you unwrapped the plane.




What you need to do is to push 7 to go to top view.
Then push 5 to go to orthographic view.
Lastly choose project from view bounds.


Before:



After:



EDIT: I misunderstood the question. The solution you are looking for is just to subdivide the plane. See this for why.